Multifactor concepts

In this chapter we discuss the multifactor concepts of confounding and randomization. The ideas underlying these concepts are then used to develop experimental designs for discrete or qualitative variables. 

Response Surfaces. 3. Basic Statistics. 4. One Experiment. 5. Two Experiments. 6. Hypothesis Testing. 7. The Variance-Covariance Matrix. 8. Three Experiments. 9. Analysis of Variance (ANOVA) for Linear Models. 10. A Ten-Experiment Example. 11. Approximating a Region of a Multifactor Response Surface. 12. Additional Multifactor Concepts and Experimental Designs. Append- ices Matrix Algebra. Critical Values of t. Critical Values of F, a = 0.05. Index. 

Experiments that will be used to estimate the behavior of a system should not be chosen in a whimsical or unplanned way, but rather, should be carefully designed with a view toward achieving a valid approximation to a region of the true response surface [Cochran and Cox (1950), Youden (1951), Wilson (1952), Mandel (1964), Fisher (1971)]. In the next several chapters, many of the important concepts of the design and analysis of experiments are introduced at an elementary level for the single-factor single-response case. In later chapters, these concepts will be generalized to multifactor, multiresponse systems. 

In previous chapters, many of the fundamental concepts of experimental design have been presented for single-factor systems. Several of these concepts are now expanded and new ones are introduced to begin the treatment of multifactor systems. 

The concept of interaction is fundamental to an understanding of multifactor systems. Much time can be lost and many serious mistakes can be made if interaction is not considered. 

The basic concepts of stability data evaluation are the same for single- vs. multifactor studies and for full- vs. reduced-design studies. Data evaluation from the formal stability studies and, as appropriate, supporting data should be used to determine the critical quality attributes likely to influence the quality and performance of the drug substance or product. Each attribute should be assessed separately and an overall assessment made of the findings for the purpose of proposing a retest period or shelf life. The retest period or shelf life proposed should not exceed that predicted for any single attribute. 

Massumi (1993) gestures in this direction The idea of causality needs work. Recursivity and cocausality (multifactor analysis) may be beginnings. But in the end, the very concept of the cause may have to go, in favor of effects and their interweavings (syndromes). Syndromes mark the limit of causal analysis. They cannot be exhaustively understood—only pragmatically altered by experimental interventions operating in several spheres of activity at once (31). 

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